Let , where , and , where . If is defined, then its domain and range, respectively,…

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let

f(x)=|x-1|

, where

f:\mathbb{R}^+\to\mathbb{R}

, and

g(x)=e^x

, where

g:[-1,\infty)\to\mathbb{R}

. If

f\circ g(x)

is defined, then its domain and range, respectively, are: (a)

(0,\infty)

and

[0,\infty)

(b)

[-1,\infty)

and

[0,\infty)

(c)

[-1,\infty)

and

[1-\frac{1}{e},\infty)

(d)

[-1,\infty)

and

[\frac{1}{e}-1,\infty)